Simplify the following expression: $ r = \dfrac{-4}{7} + \dfrac{t + 7}{4t} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4t}{4t}$ $ \dfrac{-4}{7} \times \dfrac{4t}{4t} = \dfrac{-16t}{28t} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{t + 7}{4t} \times \dfrac{7}{7} = \dfrac{7t + 49}{28t} $ Therefore $ r = \dfrac{-16t}{28t} + \dfrac{7t + 49}{28t} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-16t + 7t + 49}{28t} $ $r = \dfrac{-9t + 49}{28t}$